Pitch measurement is the measurement of the distance between two similar features. This definition applies to both the physical specimen and its image, that is, the corresponding data set collected from the specimen using a metrology or imaging system. The sample pitch is the spacing of similar elements in a specimen such as a grating. In most metrology and imaging systems, when a specimen with known sample pitch is measured or imaged, the spacing between similar features is rendered in the data set or image and the pitch in such data set or image can be used to determine the scale in the data set, for example, the magnification of the image. Thus, pitch measurement can be used for metrology or imaging system calibration to set the scale. If the scale is known in advance of data collection, a measurement of the sample pitch in a specimen with otherwise unknown pitch can be obtained from the pitch in the data set collected from the sample.
Prior art methods for pitch measurement in metrology and imaging systems fall into two categories. In the first category of prior art, measurement methods determine the pitch in the data set in a manner similar to linewidth measurement. Hence, a discussion of linewidth measurement methods follows.
In most metrology and imaging systems the signal is formed as a result of interaction of excitations with a specimen or sample and the detection of all or part of the signal generated as a result of the interaction. The excitations, in some cases referred to as probes, can be mechanical probes, electrons, photons, ions, phonons or other forms of radiation. In magnetic resonance imaging, for example, the excitations are magnetic field pulses. The detected signal can consist of charged particles, photons, phonons, or other observables such as temperature or field amplitude. What is common among most metrology and imaging systems is that they all create one, two, or three dimensional spatial images of specimen. That is, the systems produce a vector function f of the spatial coordinates r in some region of the space. The function f describing the signal can be a function of one, two, or three dimensional coordinates as f(x), f(x,y), or f(x,y,z). In addition, the function f can be a vector itself having several components. For example, a color image is represented as three functions over space: red, green and blue. These systems often produce information that is stored in computer memory in some digital format as a single column or multidimensional matrices or graphics formats for images, though the method of pitch measurement also applies to continuous signals such as photographs since they can be scanned and converted into digital forms. The data collected from metrology or imaging instruments will be referred to as a data set. This term includes gray scale images obtained from any number of systems such as CCD cameras and scanning electron microscopes. The one-dimensional data is referred to as a profile data. This term is intended to include scan lines collected with scanning probe microscopes or other scanning instruments capable of producing such data.
The features in a data set are rendered from features on the sample, though sometimes such data set features can result from noise in the scan or other electronics or from environmental factors such as vibration and other interferences. When data set features correspond to those of the sample, information about the physical features is obtained from their rendition in the collected data. In the ideal case, the feature as rendered in the data set would contain information that is identical to that of the physical feature. However, metrology and imaging systems have imperfections consisting of, but not limited to, sharpness of excitation (probe sharpness), finite interaction volume of excitation and sample, detection limits and inefficiencies, finite depth of focus, signal to noise ratio limitations, diffraction, and image distortion. In the data set, the portions of the data set formed from the sharp edges of physical sample features are smeared by these imperfections.
As an example, consider a specimen such as a diffraction grating, which consists of a series of parallel lines of equal width and equal spaces between the lines. Further assume that the metrology or imaging acquires data from a portion of the specimen consisting of parts of two or more lines. The linewidth measurement is the determination of the distance between the two edges of a physical feature, for example, the left edge and the right edge of a line in a diffraction grating. In the data set, linewidth or feature width measurement is essentially the distance between the corresponding two edges in the data set. Therefore, methods of measuring the width of a physical feature are based on methods that determine the position of two edges in the data set. With such metrology and imaging systems, the problem is in determining where the actual edge location lies along a complex waveform of the detected signal. Sometimes, the edge position in the data set is modeled based on the physics of the system and the particular experimental conditions including probe-sample interactions. But more often, the edge position in the data set is assigned by applying any number of arbitrary edge detection algorithms to the data set or a representation of the data set. Common edge detection algorithms are threshold (absolute or percentage), maximum derivative or slope, second derivative, s curve fit, linear regression, peak-to-peak distance, and centroid-to-centroid distance. All these algorithms consider a transition in the detected signal (low-to-high or high-to-low transition, or the combination of the two) and assign to some point in the signal transition interval a pixel position which is designated as the edge location in the data set, and hence corresponds to the feature edge location in the sample. Generally these methods implement subpixel interpolation schemes. The net result of smearing and arbitrary edge assignment is that the linewidth measurement tends to be biased and suffers from lack of accuracy.
The methods in the first category of prior art for pitch measurement are nearly identical to linewidth measurement as described above. The pitch in the data set is measured as the difference between the locations of two similar edges of the same type in the data set. That is, a left-edge to left-edge distance or a right-edge to right-edge distance, or peak-to-peak distance and so on. This type of prior art is depicted in FIG. 1, where the original data set (not shown) is reduced to a one-dimensional profile data 2. In this example, transitions in the profile data represent the edges in the sample. Two similar edge regions 12 and 14 (both left edges in this example) in the profile data are determined. The pixel positions 16 and 18 of the two similar edges 12 and 14 are considered. The positions 16 and 18 are determined by application of any one of edge detection algorithms identical to the algorithms used for edge position determination in linewidth measurement listed before. The pitch in the data set is then calculated as the difference between the position of two similar edges in the data set, P=r2−r1, where P is the measured pitch in the data set, r1 is the pixel location 16 of the first edge as determined by a particular algorithm, and r2 is the pixel location 18 of the second edge as determined by the same algorithm. The edge pixel positions are often determined to a subpixel range of values by interpolation. In summary, the first category of prior art requires determination of two similar edge positions in the data set.
The smearing of the features in the image or data set affects linewidth and pitch measurements differently. In a linewidth measurement, the results depend on the magnitude of the broadening of the edge in the data set as caused by the particular physical effects and experimental conditions that cause the broadening of the edges at the time of data collection. This fact is well known, and for this reason, image magnification calibration to the feature with a known width is not recommended and in modem metrology tools, instrument image magnification calibration is accomplished with measurement of pitch of a specimen with known physical pitch. Due to the fact that the smearing alters the two similar edges in the data set in a similar manner, the effects of broadening of the two edges tend to cancel out in pitch measurement. For this reason pitch measurements are referred to as self-compensating or unbiased. More specifically, such pitch measurements do not require a physical model for edge determination in order to be accurate and are far less sensitive to image imperfections arising from finite probe size (excitation-sample interaction volume). However, it is known in the prior art that all pitch measurement algorithms are not identical in performance. At issue is the undesired contribution of the measurement algorithm to the uncertainty of the pitch measurement. This contribution limits the precision or repeatability with which the pitch can be measured, and consequently the precision with which the scale of the metrology or imaging system can be calibrated.
The National Institute of Science and Technology (NIST) has developed a version of the pitch measurement algorithm belonging to the first category of prior art for use in scanning electron microscopes. This algorithm is described in an article entitled “A New Algorithm for the Measurement of Pitch in Metrology Instruments”, N. F. Zhang et al, Proceedings of SPIE, Vol. 2725, pp. 147-158, 1996. In the NIST algorithm, the two edge locations are determined using regression to fit two straight lines to the signal in the transition regions for each edge, but the method places an additional restriction on the slopes of the lines fitted to the two similar edges in the data. The fitted lines must have identical slopes in the regression.
The second category of prior art consists of methods that apply Fourier transform to the data set as disclosed in U.S. Pat. No. 4,818,873 issued to Glen A. Harriot. These methods determine the location of the peak in the amplitude of the Fourier transform of the data set or detected signal. Since the peak in Fourier Transform of the signal corresponds to the fundamental spatial frequency in the image or data set, the position of this peak is assigned the special frequency of the pitch in the data set. This method works well for low magnification images containing several edge replications in the data set. When few repetitions of the periodic structure are present in the data set, the measurement method lacks precision.
While the prior art methods of pitch measurement have proved useful, they suffer from several disadvantages. The pitch measurement algorithms that are based on edge detection are more sensitive to noise and hence not very precise in determining the pitch. In addition, they require as input to the measurement, the conditions for edge detection, including specification of pixel search range intervals for finding each edge. In automated pitch measurement, there exists a requirement that the image of the features be aligned to the search ranges before applying the edge detection algorithm, otherwise the measurement will fail.
Accordingly, there is a need for methods of measuring pitch in the data set that can overcome or eliminate such inefficiencies and disadvantages, can be easier to use, can result in measurements that are more precise, more robust, more versatile, and do not require, but can accommodate, search ranges and can be extended to higher data dimensions.